IB Maths AI HL AI 1.3 Exponents, logarithms and equations questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

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Question 1

Paper 1Medium6 marks

A fountain jet is modelled, for $0\leq x\leq 6$ by

h=ax^2+bx+c,

where $x$ is the horizontal distance from the nozzle, in metres, and $h$ is the height above the ground, in metres. The model passes through the points shown.

$x$	0	3	6
$h$	1.20	4.80	5.10

(a)

Use technology to determine the values of $a$ $b$ and $c$ giving each to at least three significant figures.

[3]

(b)

Hence determine the horizontal distance(s), in the interval $0\leq x\leq 6$ at which the model gives $h=3.00$ Give your answer to the nearest $0.01$ m.

[3]

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